Particle System does not stick to the mesh if the mesh is moving (global,local coordinate-system?)
It sounds like an issue you get when the modifiers are in the wrong order.



The modifiers are applied from the top down. In this example the particles are generated then the armature deforms the mesh which leaves the particles behind.

Check that the modifier for the particles or smoke is last in the list. Use the little up/down arrows to the right re-arrange the order.

You may want to alter the gravity settings for the particles to alter their direction. Particles usually fall down by default, you also only need a lifetime of one frame for them to generate smoke. Force fields can also be used to control the flow of particles and smoke.